The special atom space and Haar wavelets in higher dimensions
Autor: | Geraldo De Souza, M.M. Ndiaye, N. Djitte, Eddy Kwessi |
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Rok vydání: | 2020 |
Předmět: |
42b05
30b50 high dimension lcsh:Mathematics General Mathematics haar wavelets 010102 general mathematics Haar 30e20 lcsh:QA1-939 Space (mathematics) 01 natural sciences analytic function 010101 applied mathematics Wavelet special atom Quantum mechanics Atom (measure theory) 42b30 0101 mathematics Mathematics Analytic function |
Zdroj: | Demonstratio Mathematica, Vol 53, Iss 1, Pp 131-151 (2020) |
ISSN: | 2391-4661 |
Popis: | In this note, we will revisit the special atom space introduced in the early 1980s by Geraldo De Souza and Richard O’Neil. In their introductory work and in later additions, the space was mostly studied on the real line. Interesting properties and connections to spaces such as Orlicz, Lipschitz, Lebesgue, and Lorentz spaces made these spaces ripe for exploration in higher dimensions. In this article, we extend this definition to the plane and space and show that almost all the interesting properties such as their Banach structure, Hölder’s-type inequalities, and duality are preserved. In particular, dual spaces of special atom spaces are natural extension of Lipschitz and generalized Lipschitz spaces of functions in higher dimensions. We make the point that this extension could allow for the study of a wide range of problems including a connection that leads to what seems to be a new definition of Haar functions, Haar wavelets, and wavelets on the plane and on the space. |
Databáze: | OpenAIRE |
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